997SM - FISICA DELLA MATERIA CONDENSATA I 2025
Schema della sezione
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The "Condensed Matter Physics I" Course is given in the first term, for a total number of 48 hours (6 credits). It is compulsory for the Condensed Matter Physics training track.
The course will provide theoretical concepts fundamental to understanding the behaviour of electrons in crystals and the basic tools to treat them, both in problems solvable with classical methods and those requiring a quantum treatment. Main topics: models for non-interacting electrons; crystalline lattices and structures; independent electrons in a periodic potential (Bloch electrons) and energy bands; semiconductors; magnetism.
LECTURES:
will be given in English or Italian according whether foreign students are present or not, and upon agreement with students; textbooks, lecture notes and other materials are in English.
Schedule (from Sept. 22 to Dec. 19, 2025) https://orari.units.it/agendaweb/index.php?view=easycourse&_lang=en&include=attivita => Course "Fisica della Materia Condensata I":
Wed 9-11 am, Room D (starting at 9:15)
Fri 9-11 am, Room D (starting at 9:15)
Fri 4-5 pm (mainly for additional exercises, to be decided weekly), Room B
in Building F (via Valerio, 2)
Lectures are recorded and collected on MS TEAMS platform; for the access code: https://www.units.it/catalogo-della-didattica-a-distanza
TEXTBOOKS:N. Ashcroft, N D. Mermin, Solid State Physics, Saunders College (1976) (main text).
G. Grosso and G. Pastori Parravicini, Solid State Physics, Academic Press (2000)
C. Kittel, Introduction to Solid State Physics, Wiley (1996).
L. Mihaly e M.C. Martin, Solid State Physics: Problems and Solutions, Wiley (1996).EXAMS:
The exam includes written & oral parts
Six dates for the final written test (2 dates in Jan/Feb 2026; 2 in June/July 2026; 2 in August/September 2026) will be scheduled; for the calendar see: https://orari.units.it/agendaweb/index.php?view=easytest&include=homepage&_lang=en (written tests are labelled as "prova parziale").NEXT DATES (JAN-FEB 2026) room D Building F via Valerio 2:- Thu 15/01/2026 at 8:30-13 (oral)- Mon 19/01/2026 at 8:30-13 (oral)- Wed 21/01/2026 at 9-11:30 (I final written test)- Mon 26/01/2026 at 8:30-13 (oral)- Mon 09/02/2026 at 9-11:30 (II final written test)- Thu 12/02/2026 at 8:30-13 (oral)2 intermediate written tests are proposed; who pass them successfully, afford directly the oral part (this is valid till the summer session included).The oral exam must be done within few days after the written test (depending on the number of candidates).
Typically 2.5 hours are available for the final written tests (1.5 hours for the intermediate tests). Books and lecture notes can be used during the written tests and exams.
Exams can be given either in English or in Italian (no penalties or rewards for one or the other choice)
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Introduction to the Course; references. Basic assumptions of the Drude model for metals (noninteracting and free electrons; collisions, damping term, relaxation time; application of the kinetic theory of gases); DC electrical conductivity; Hall effect.
AC electrical conductivity; dielectric function and plasma frequency. Thermal conductivity and Wiedemann-Franz law. (Ashcroft-Mermin, Ch. 1)
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Fermi-Dirac distribution. Ground state of free and indep. electron gas; Fermi momentum; energy; temperature; prediction for the pressure exerted by electrons, bulk modulus and comparison with experiments.
Integrals in energy and k space: density of states (see also these notes). Chemical potential. Use of Sommerfeld expansion; electronic contribution to the specific heat.
Exercises.
[Ashcroft-Mermin, Ch. 2 - Exercises n. 1, 3, 4]
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Introduction to lattice structures: Bravais lattices and crystalline structures in real space. Lattices with basis (generalities; examples about the conventional cells of the cubic lattices; other relevant examples: diamond, graphene, graphite). Packing fraction.
Other examples of Bravais lattices with basis: zincblende, rocksalt, wurzite (one slide). Wigner-Seitz cells.
Reciprocal lattices. Families of lattice planes. Miller indices.
Brillouin zone.
X-ray diffraction: Bragg and von Laue. Structure factor.
[Ashcroft & Mermin, Ch. 4, 5, 6]
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Aperto: mercoledì, 15 ottobre 2025, 11:00Chiusura: mercoledì, 14 ottobre 2026, 00:00
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Periodic potential: Bloch theorem, I and II [22 Oct.] proof (Ch. 8).
Consequences of the Block theorem: crystalline momentum; velocity; energy bands. (Ch. 8) [24 Oct.]
Fermi surfaces. Density of states (DoS): different approaches. Derivation of the DoS using the properties of the delta-function . Van Hove singularities. (Ch. 8) [24 Oct.]
Divergences in the DOS integrals - Van Hove singularities in 1D, 2D, 3D. Exercise n. 2 Ch. 8 of A&M [29 Oct]Brillouin zones, band folding and band indices [29 Oct]Band plots in reduced zone / periodic / extended representation Fermi surfaces and their folding into the first Brillouin zone (end of Ch. 8]. [31 Oct]"Empty lattice" band structure in 1D and FCC [31 Oct]
A nice applet for plotting the "empty lattice" bands: PHY.K02UF Molecular and Solid State Physicshttp://lampx.tugraz.at/~hadley/ss1/emfield/empty/empty.phpComments on selected slides on: band structures, Fermi surfaces, DOS [31 Oct]Calculation of k_F in the "empty lattice" model and comparison of the Fermi surface with the Brillouin zone [31 Oct] -
5. Approximate treatment of electrons in a periodic potential: effects of a weak potential (7,12 Nov. 2025)
Brillouin zones. Folding of Fermi spheres in case of "empty" lattice model: Example for a square lattice with different numbers of valence electrons per cell
Effects of a weak perturbing potential (nearly free electrons): non degenerate case; degenerate case (two-levels system) (A&M, ch. 9)
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6. Approximate treatment of electrons in a periodic potential: tight-binding approach (14(2h), 19(exercises) Nov. 2025)
The tight-binding approach: introduction, general formulation; the simplified case of s-band arising from a single atomic s-level. Tight-binding in crystals with inversion symmetry; band dispersion (A&M, ch. 10).
Bloch sums and their periodicity in direct space depending to k.
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Validity of semicl. dynamics. Equations of motions. Filled bands. Holes.
Orbits in r and k space. Motion of electrons in uniform and static electric fields. Motion of electrons in uniform and static magnetic fields; electron orbits, hole orbits, open and closed orbits. Period of closed orbits.
(Chap 12 of A&M book)
Additional material: Fermi surfaces of real metals (examples from www.phys.ufl.edu/fermisurface)
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Issues discussed in class and requested for the exam:
Boltzmann eq.: Ch. 13 only Introduction; Ch. 16: Sect. IV (The Boltzmann eq.); Sect. I (Source of el. scattering); Ch. 16: Sect. II (Scattering prob. and relaxation time); Sect. III (Rate of change of the distribution function due to collisions). ( lecture notes, see parts 1-4). Ch. 13 Sect. IV (DC Electrical conductivity) ( lecture notes, see part 5)
Issues not discussed in class, optional, not requested for the exam:
AC Electric conductivity (Ch. 13 Sect. IV); transport in anisotropic materials (lecture notes, see parts 5-6)
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Some exercises on Bloch electrons, bands, semiclassical model of electron dynamics. (5 (2h), 12(1h morning + 1 h afternoon), 17 Dec.2025)
test 16/01/2017 ex 3test 19/12/2013 ex 3Wed. 17/12/25:test 14/01/2013 ex 1test 16/01/02017 - mod. II - ex 1test 08/02/2016 ex 2 (similar to test 23/01/2015 ex 2)test 20/09/2017 ex 2test 02/12/2008 ex 3test 20/09/2018 ex 3 -
Homogeneous semiconductors: materials (elemental and compounds), typical band structures, intrinsic and extrinsic semiconductors. Intrinsic case: number of carriers in thermal equilibrium. Extrinsic semiconductors: donor and acceptor levels. (Ch. 28; excluding: eqs. 28.23-28.27)